Teach First said it has been made aware of job adverts but has not worked with the recruitment agency to post the adverts or fill the positions advertised.

A spokesperson added: “We will be looking into the adverts further.”

Michael Merrick, a teacher in Cumbria who spotted the advert, said it was appalling to only ask for Teach First recruits.

He said: “For outstanding teachers and leaders who have come through other training routes to be ruled out of employment opportunities on solely that basis seems both unjust and, in light of the recruitment challenge more generally, an odd narrowing of the field.

“Adverts like this can give the impression that there is a two-tier system within teaching, with the outstanding candidates who did not come through Teach First training routes being judged as less capable or desirable than those who did. This is both unjust and untrue.”

Mr Merrick added that there is an implication in some advertising that Teach First has a monopoly on the most talented.

“It would appear this view is filtering down to employment, rendering those who came through other routes as second-class teachers in the jobs market,” he said.

Dr Mary Bousted, general secretary of the Association of Teachers and Lecturers, said the advert was a “curious” way of recruiting teachers, which limited the potential applicant pool at a time of high teacher shortages.

“The weakening of leadership support, through the virtual demise of the National College for Teaching and Leadership, may lead to others making similar recruitment decisions, which is a short-term, divisive and potentially discriminatory approach which we would urge schools to avoid,” said Dr Bousted.

“Teach First is a strong programme but surely it would be fairer for their graduates to compete equally with others from other training routes for positions, and schools can then pick those with the best combination of experience, skills and training to do the job, from whatever route they come.”